Adaptive modeling of changed states in predictive condition monitoring

ABSTRACT

An improved empirical model-based surveillance or control system for monitoring or controlling a process or machine provides adaptation of the empirical model in response to new operational states that are deemed normal or non-exceptional for the process or machine. An adaptation decision module differentiates process or sensor upset requiring alerts from new operational states not yet modeled. A retraining module updates the empirical model to incorporate the new states, and a pruning technique optionally maintains the empirical model by removing older states in favor of the added new states recognized by the model.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims benefit of U.S. Provisional ApplicationNo. 60/262,747, filed Jan. 19, 2001.

FIELD OF THE INVENTION

[0002] The present invention relates to monitoring machines and physicalprocesses for early detection of impending equipment failure or processdisturbance and on-line, continuous validation of sensor operation. Moreparticularly, the invention relates to systems and methods governingadaptation of empirical models to changed conditions in such monitoringsystems, and resolution of process change from sensor change.

BACKGROUND OF THE INVENTION

[0003] A variety of new and advanced techniques have emerged inindustrial process control, machine control, system surveillance, andcondition based monitoring to address drawbacks of traditionalsensor-threshold-based control and alarms. The traditional techniquesdid little more than provide responses to gross changes in individualmetrics of a process or machine, often failing to provide adequatewarning to prevent unexpected shutdowns, equipment damage, loss ofproduct quality or catastrophic safety hazards.

[0004] According to one branch of the new techniques, empirical modelsof the monitored process or machine are used in failure detection andcontrol. Such models effectively leverage an aggregate view ofsurveillance sensor data to achieve much earlier incipient failuredetection and finer process control. By modeling the many sensors on aprocess or machine simultaneously and in view of one another, thesurveillance system can provide more information about how each sensor(and its measured parameter) ought to be behaving. An example of such anempirical surveillance system is described in U.S. Pat. No. 5,764,509 toGross et al., the teachings of which are incorporated herein byreference. Therein is described an empirical model using a similarityoperator against a reference library of known states of the monitoredprocess, and an estimation engine for generating estimates of currentprocess states based on the similarity operation, coupled with asensitive statistical hypothesis test to determine if the currentprocess state is a normal or abnormal state. Other empirical model-basedmonitoring systems known in the art employ neural networks to model theprocess or machine being monitored.

[0005] Such empirical model-based monitoring systems require as part ofinstallation and implementation some baseline data characterizing thenormal operation of the process or machine under surveillance. Theempirical model embodies this baseline normal operational data, and isonly as good as the data represents normal operation. A big challenge tothe success of the empirical model in the monitoring system, therefore,is to provide sufficiently representative data when building theempirical model. In practice, this is possibly the greatest hurdle forsuccessful implementation of empirical model-based surveillance systems.

[0006] A first problem is whether to use data from merely a like processor the identical process with the one being monitored. This isespecially significant when monitoring a commodity machine, that is, amachine that will be mass-produced with on-board condition monitoring.Under such circumstances, it may not be possible or practical to gathernormal operational data from each machine to build unique empiricalmodels beforehand. What is needed is a way of building a general modelinto the newly minted machines, and allowing the model to adapt to theunique tolerances and behavior of each particular machine in the field.

[0007] A second problem presents itself as the monitored process ormachine settles with age, drifting from the original normal baseline,but still being in good operational condition. It is extremely difficultto capture such eventually normal operational data from a process ormachine for which that would currently not constitute normal operation.What is then needed is a way for the empirical model to adapt toacceptable changes in the normal operation of the process or machinewith age, without sacrificing the monitoring sensitivity thatnecessitated the empirical model approach in the first place.

[0008] A third problem exists where it is not possible to capture thefull normal operational range of sensor data from the process due to thefinancial or productive value of not disrupting the process. Forexample, in retrofitting an existing industrial process with empiricalmodel-based monitoring, it may not be economically feasible toeffectively take the process off-line and run it through its manyoperational modes. And it may be months or years before all theoperational modes are employed. Therefore, what is needed is a way toadapt the empirical model as the operational modes of the process ormachine are encountered for the first time.

[0009] In summary, in order for an empirical model based processsurveillance system to function reliably, the data used to generate themodel should span the full process operating range. In many cases thatdata are not available initially. Therefore, model adaptation is neededto keep the model up-to-date and valid. But adaptation imposessignificant hurdles of its own. One such hurdle is determining exactlywhen to start adapting the model, especially for dynamic non-linearprocesses. While in some cases human intervention can be relied upon tomanually indicate when to adapt, in the vast majority of circumstancesit is desirable to automate this determination. Another such hurdle isdetermining when to stop adapting the model and reinitiate process ormachine surveillance. Yet another problem is to distinguish the need foradaptation from a process upset or a sensor failure that should beproperly alarmed on. It is highly desirable to avoid “bootstrapping” ona slow drift fault in the process, for example. Yet another problem isto avoid adapting during a period of transition between one stable stateand another, during which sensor data may not be typicallyrepresentative of either any old state or a new state of normaloperation of the process or machine. Yet another problem in adapting theempirical model is that the model may grow and become less accurate orless specific due to the addition of new states. Therefore, it would bebeneficial to have a way of removing least commonly encountered statesfrom the model while adding the newly adapted states.

SUMMARY OF THE INVENTION

[0010] The present invention provides an improved empirical model-basedsystem for process or machine control and condition-based monitoring.

[0011] This invention is a method and apparatus for deciding when anempirical model of a process or machine should be adapted to encompasschanging states in that process or machine, as measured by sensors,derived variables, statistical measures or the like. The technique isbased on the information provided by a similarity measurement technologyand statistical decisioning tools. This system has a secondcharacteristic in that it determines when to stop the model adaptationprocess. This system has a third capability of distinguishing betweenprocess change and instrument change cases.

[0012] In a process or machine that is fully instrumented with sensorsfor all parameters of interest, sensor data is collected for all regimespossible of expected later operation of the same or similar processes ormachines. This collected data forms a history from which the inventivesystem can “learn” the desired or normal operation of the process ormachine, using training routines that distill it to a representative setof sensor data. Using this representative training set of sensor data,the present invention is able to monitor the process or machine inreal-time operation (or in batch mode, if preferred), and generateestimates for all the sensors, including certain of the sensors forwhich historic data was collected, but which have failed or which wereremoved from the process or machine. The present invention can beemployed as a means of adapting the representative set of sensor data toaccommodate changes to the monitored system that are considered withinthe acceptable or normal range of operation.

[0013] The apparatus of the present invention can be deployed as anelectrically powered device with memory and a processor, physicallylocated on or near the monitored process or machine. Alternatively, itcan be located remotely from the process or machine, as a module in acomputer receiving sensor data from live sensors on the process ormachine via a network or wireless transmission facility.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The novel features believed characteristic of the invention areset forth in the appended claims. The invention itself, however, as wellas the preferred mode of use, further objectives and advantages thereof,is best understood by reference to the following detailed description ofthe embodiments in conjunction with the accompanying drawings, wherein:

[0015]FIG. 1 illustrates a block diagram of the invention for adaptingan empirical model-based monitoring system for an instrumented processor machine;

[0016]FIG. 2 illustrates a method for creating a representative“training” data set from collected sensor data for use in the invention;

[0017]FIG. 3 illustrates a flowchart for creating a representative“training” data set from collected sensor data for use in the invention;

[0018]FIG. 4 illustrates the computation of one of the similarityoperators employed in the present invention;

[0019]FIG. 5 illustrates a chart of global similarity values showing amove into transition out of one state of operation by the monitoredprocess or machine;

[0020]FIG. 6 illustrates a chart of global similarity values showingcompletion of a transition phase into another potentially unmodeledstate of operation by the monitored process or machine;

[0021]FIG. 7 illustrates a chart of global similarity values showing atransition from one modeled state to another modeled state of themonitored process or machine;

[0022]FIG. 8 illustrates a chart of global similarity values showing atransition from one modeled state to another potentially unmodeled stateof the monitored process or machine;

[0023]FIG. 9A symbolically illustrates a similarity operation between acurrent snapshot and the reference library snapshots; and

[0024]FIG. 9B illustrates a chart of similarity scores for comparisonsin FIG. 9A, with a highest similarity indicated.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] Turning to FIG. 1, a block diagram is shown of the inventiveadaptive empirical model-based monitoring system. A process or machine105 is instrumented with sensors for detecting various physical,statistical, qualitative or logical parameters of the process or machineoperation. These are typically provided to the inventive system via aninput bus 108, exemplified by a FieldBus type bus in a process controlsystem in an industrial plant. The data representing the current stateof the process or machine 105 is fed from input bus 108 to an estimationengine 111, which is coupled to a reference library 114 of past datarepresentative of normal or acceptable states of operation of theprocess or machine. Together, the estimation engine 111 and thereference library 114 comprise the empirical model 117 that models theprocess or machine.

[0026] In standard monitoring mode, the sensor data from input bus 108are also provided to a differencing engine 120 that is disposed toreceive estimates of the current state generated by the empirical model117 in response to input of the actual current state of the process ormachine. The differencing engine subtracts for each sensor involved theestimate from the actual, and provides these individual outputs to astatistical testing module 122 that determines whether the estimate andactual values are the same or statistically different, in which case analert is displayed or otherwise provided to further automated controlsystems. By way of example, the statistical testing module 122 can bedisposed to perform a sequential probability ratio test (SPRT) on eachof the differenced sensor signals coming from differencing engine 120,to provide alerts for each signal that is not “normal” or acceptable. Inthis manner, monitoring of the process or machine is carried out basedon the empirical model, providing greater sensitivity and improved leadwarning time for failures.

[0027] Current sensor data can also be provided to adaptation decisionmodule 125. According to the present invention, this module makes adetermination of whether the current snapshot of sensor data from theprocess or machine 105 represents a process upset or a sensor failure,or in contrast represents the start of a transition to a new operationalstate requiring adaptation of the model, or the stop of a transition toa new operational state. Upon recognizing the start of such atransition, the alert-type output of the empirical model-basedmonitoring can be temporarily suspended to avoid inundating a humanoperator or a downstream control system with unnecessary alertinformation. Upon recognizing the stop of the transition, the adaptationdecision module 125 can enable a retraining module 128 disposed to carryout the actual changes to the reference library 114 necessary to effectadaptation of the model. After the stop of the transition, the processor machine 105 is expected to be in a stabilized new state that may notbe represented in the reference library 114. After the transition iscomplete, the adaptation decision module 125 initiates via theretraining module 128 capture of new snapshots of live data to augmentthe reference library 114. In the event that the reference library growstoo large, or is desirably maintained at a certain size (e.g., forperformance considerations), the vector removal module 131 can weed outold snapshots from the reference library according to certain criteria.Upon completion of the adaptation of the reference library, on-linemonitoring is commenced again.

[0028] The invention provides a fully automated model adaptationdecision-making technique for condition based monitoring of a machine orprocess. The adaptation decision module can employ the same similarityoperator techniques that can be employed in the empirical model forgenerating estimates, as discussed below. Accordingly, the currentsensor snapshot from the input bus 108 is compared using the similarityoperator to the estimate generated in response thereto by the estimationengine 111 to generate a similarity score called global similarity forpurposes hereof. This global similarity is itself a signal that can bemonitored and processed snapshot over snapshot. The behavior of theglobal similarity is one means by which the inventive module candistinguish the need for adaptation from a mere process or sensor upset.

[0029] Turning now first to the regular monitoring mode of the inventivesurveillance system, an empirical model-based method and system formonitoring a process or machine is described in the aforementioned U.S.Pat. No. 5,764,509 to Gross et al. Implementing such a monitoring systemcomprises two stages, a first stage for building the empirical model(also known as “training”), and a second stage of turning livemonitoring on. Other empirical models that train on known data couldalso be employed, such as neural networks, but for purposes ofillustration, an empirical model along the lines of the Gross patent asa baseline will be described.

[0030] A method for training the empirical model is graphically depictedin FIG. 2, wherein collected historic sensor data for the process ormachine is distilled to create a representative training data set, thereference library. Five sensor signals 202, 204, 206, 208 and 210 areshown for a process or machine to be monitored, although it should beunderstood that this is not a limitation on the number of sensors thatcan be monitored using the present invention. The abscissa axis 215 isthe sample number or time stamp of the collected sensor data, where thedata is digitally sampled and the sensor data is temporally correlated.The ordinate axis 220 represents the relative magnitude of each sensorreading over the samples or “snapshots”. Each snapshot represents avector of five elements, one reading for each sensor in that snapshot.Of all the previously collected historic sensor data representing normalor acceptable operation, according to this training method, only thosefive-element snapshots are included in the representative training setthat contain either a minimum or a maximum value for any given sensor.Therefore, for sensor 202, the maximum 225 justifies the inclusion ofthe five sensor values at the intersections of line 230 with each sensorsignal, including maximum 225, in the representative training set, as avector of five elements. Similarly, for sensor 202, the minimum 235justifies the inclusion of the five sensor values at the intersectionsof line 240 with each sensor signal.

[0031] Selection of representative data is further depicted in FIG. 3.Data collected representing normal operation has N sensors and Lobservations or snapshots or temporally related sets of sensor data thatcomprise an array X of N rows and L columns. In step 304, a counter ifor element number is initialized to zero, and an observation orsnapshot counter t is initialized to one. Two arrays max and min forcontaining maximum and minimum values respectively across the collecteddata for each sensor are initialized to be vectors each of N elementswhich are set equal to the first column of X. Two additional arrays Tmaxand Tmin for holding the observation number of the maximum and minimumvalue seen in the collected data for each sensor are initialized to bevectors each of N elements, all zero.

[0032] In step 307, if the sensor value of sensor i at snapshot t in Xis greater than the maximum yet seen for that sensor in the collecteddata, max(i) is update to equal the sensor value and Tmax(i) stores thenumber t of the observation in step 310. If not, a similar test is donefor the minimum for that sensor in steps 314 and 317. The observationcounter t is incremented in step 320. In step 322, if all theobservations have been reviewed for a given sensor (t=L), then t isreset and i is incremented (to find the maximum and minimum for the nextsensor) in step 325. If the last sensor has been finished (i =N), step328, then redundancies are removed and an array D is created from asubset of vectors from X.

[0033] First, in step 330, counters i and j are initialized to one. Instep 333, the arrays Tmax and Tmin are concatenated to form a singlevector Ttmp having 2N elements. These elements are sorted into ascending(or descending) order in step 336 to form array T. In step 339, holdertmp is set to the first value in T (an observation number that containsa sensor minimum or maximum). The first column of D is set equal to thecolumn of X corresponding to the observation number that is the firstelement of T. In the loop starting with decision step 341, the ithelement of T is compared to the value of tmp that contains the previouselement of T. If they are equal (the corresponding observation vector isa minimum or maximum for more than one sensor), it has already beenincluded in D and need not be included again. Counter i is incrementedin step 350. If they are not equal, D is updated to include the columnfrom X that corresponds to the observation number of T(i) in step 344,and tmp is updated with the value at T(i). The counter j is thenincremented in step 347. In step 352, if all the elements of T have beenchecked, then the distillation into training set D has finished, step355.

[0034] A variety of empirical models are considered to be the object ofthe present adaptive decisioning and retraining invention, includingneural networks, fuzzy logic models, and the like. All these empiricalmodels employ data from the process or machine under surveillance tomodel and thereby monitor the process or machine. All are subject to theshortcomings of the historic data provided when the models are built, inview of the graceful aging, settling or previously unencountered statesof the monitored process or machine. By way of an example of applyingthe methods of the current invention, the empirical modeling techniqueof the aforementioned patent to Gross et al., will be described. Thisempirical modeling technique uses a similarity operator, which is alsoan inventively employed in the present invention in the form of globalsimilarity and other adaptation decisioning techniques described herein.Generally, a similarity operation provides a scalar similarity scorescaled between one extreme (typically “1” for “identical”) and anotherextreme (typically “zero” for “completely dissimilar”), upon acomparison of two numbers. More particularly, this can be adapted forcomparing two vectors having equal numbers of elements, where asimilarity score is yielded for comparing each like element of the twovectors, and then averaging or otherwise statistically combining thesimilarity scores into one vector-to-vector similarity score.

[0035] The calculations for the similarity operation are now describedin detail below. In what follows, the subscript “in” generallycorresponds to the actual snapshot obtained from the input bus 108,which may comprise for example ten real time correlated sensors, and thesubscript “out” generally corresponds to estimates generated by theestimation engine 111. The reference library 114 comprises a series ofsnapshots selected according to the above-described training method,each snapshot being a vector of sensor data, arranged like the inputsnapshot is arranged. To follow the example then, the reference librarywould comprise vectors made up of ten elements each. This referencelibrary will also be referred to as the matrix D.

[0036] The step of providing a representative training set according tothe description above results in a matrix D of values, having ten rows(corresponding to the ten parameters measured on the process or machine)and a sufficient number n of columns (sets of simultaneous or temporallyrelated sensor readings) to properly represent the full expected dynamicoperating range of the process or machine. While the order of thecolumns does not matter in D, the correspondence of rows to particularsensors must be fixed.

[0037] Then, using y_(in) to designate a vector (having ten elements inthis example) corresponding to the input snapshot from input bus 108, avector y_(out) is generated as the estimate from estimation engine 111having ten elements, according to:

{right arrow over (y)} _(out) ={overscore (D)}·{overscore (W)}

[0038] where W is a weight vector having as many elements N as there arecolumns in D, generated by:$\overset{\rightarrow}{W} = \frac{\underset{\rightarrow}{\hat{W}}}{\left( {\sum\limits_{j = 1}^{N}{\hat{W}(j)}} \right)}$

$\underset{\rightarrow}{\hat{W}} = {\left( {{\overset{\_}{D}}^{T} \otimes \overset{\_}{D}} \right)^{- 1} \cdot \left( {{\overset{\_}{D}}^{T} \otimes {\overset{\rightarrow}{y}}_{in}} \right)}$

[0039] where the similarity operation is represented by the circle withthe cross-hatch inside it. The superscript “T” here represents thetranspose of the matrix, and the superscript “−1” represents the inverseof the matrix or resulting array. Importantly, there must be rowcorrespondence to same sensors for the rows in D, y_(in) and y_(out).That is, if the first row of the representative training set matrix Dcorresponds to values for a first sensor on the machine, the firstelement of y_(in) must also be the current value (if operating inreal-time) of that same first sensor.

[0040] The similarity operation can be selected from a variety of knownoperators that produce a measure of the similarity or numericalcloseness of rows of the first operand to columns of the second operand.The result of the operation is a matrix wherein the element of the ithrow and jth column is determined from the ith row of the first operandand the jth column of the second operand. The resulting element (i,j) isa measure of the sameness of these two vectors. In the presentinvention, the ith row of the first operand generally has elementscorresponding to sensor values for a given temporally related state ofthe process or machine, and the same is true for the jth column of thesecond operand. Effectively, the resulting array of similaritymeasurements represents the similarity of each state vector in oneoperand to each state vector in the other operand.

[0041] By way of example, one similarity operator that can be usedcompares the two vectors (the ith row and jth column) on anelement-by-element basis. Only corresponding elements are compared,e.g., element (i,m) with element (m,j) but not element (i,m) withelement (n,j). For each such comparison, the similarity is equal to theabsolute value of the smaller of the two values divided by the larger ofthe two values. Hence, if the values are identical, the similarity isequal to one, and if the values are grossly unequal, the similarityapproaches zero. When all the elemental similarities are computed, theoverall similarity of the two vectors is equal to the average of theelemental similarities. A different statistical combination of theelemental similarities can also be used in place of averaging, e.g.,median.

[0042] Another example of a similarity operator that can be used can beunderstood with reference to FIG. 4. With respect to this similarityoperator, the teachings of U.S. Pat. No. 5,987,399 to Wegerich et al.are relevant, and are incorporated in their entirety by reference. Foreach sensor or physical parameter, a triangle 404 is formed to determinethe similarity between two values for that sensor or parameter. The base407 of the triangle is set to a length equal to the difference betweenthe minimum value 412 observed for that sensor in the entire trainingset, and the maximum value 415 observed for that sensor across theentire training set. An angle Ω is formed above that base 407 to createthe triangle 404. The similarity between any two elements in avector-to-vector operation is then found by plotting the locations ofthe values of the two elements, depicted as X₀ and X₁ in the figure,along the base 407, using at one end the value of the minimum 412 and atthe other end the value of the maximum 415 to scale the base 407. Linesegments 421 and 425 drawn to the locations of X₀ and X₁ on the base 407form an angle θ. The ratio of angle θ to angle Ω gives a measure of thedifference between X₀ and X₁ over the range of values in the trainingset for the sensor in question. Subtracting this ratio, or somealgorithmically modified version of it, from the value of one yields anumber between zero and one that is the measure of the similarity of X₀and X₁.

[0043] Any angle size less than 180 degrees and any location for theangle above the base 407 can be selected for purposes of creating asimilarity domain, but whatever is chosen must be used for allsimilarity measurements corresponding to that particular sensor andphysical parameter of the process or machine. Conversely, differentlyshaped triangles 404 can be used for different sensors. One method ofselecting the overall shape of the triangle is to empirically test whatshape results in consistently most accurate estimated signal results.

[0044] For computational efficiency, angle Ω can be made a right angle(not depicted in the figure). Designating line segment 431 as a height hof the angle Ω above the base 407, then angle θ for a givenelement-to-element similarity for element i is given by:$\theta_{i} = {{\tan^{- 1}\left( \frac{h}{X_{1}(i)} \right)} - {\tan^{- 1}\left( \frac{h}{X_{0}(i)} \right)}}$

[0045] Then, the elemental similarity is:$s_{i} = {1 - \frac{\theta_{i}}{\pi/2}}$

[0046] As indicated above, the elemental similarities can bestatistically averaged or otherwise statistically treated to generate anoverall similarity of a snapshot to another snapshot, as if called foraccording to the invention.

[0047] Yet another class of similarity operator that can be used in thepresent invention involves describing the proximity of one state vectorto another state vector in n-space, where n is the dimensionality of thestate vector of the current snapshot of the monitored process ormachine. If the proximity is comparatively close, the similarity of thetwo state vectors is high, whereas if the proximity is distant or large,the similarity diminishes, ultimately vanishingly. By way of example,Euclidean distance between two state vectors can be used to determinesimilarity. In a process instrumented with 20 sensors for example, theEuclidean distance in 20-dimensional space between the currentlymonitored snapshot, comprising a 20 element state vector, and each statevector in the training set provides a measure of similarity, as shown:$S = \frac{1}{\left\lbrack {1 + \frac{\left. ||{\overset{\rightarrow}{x} - \overset{\rightarrow}{d}} \right.||^{\lambda}}{c}} \right\rbrack}$

[0048] wherein X is the current snapshot, and d is a state vector fromthe training set, and λ and c are user-selectable constants.

[0049] Turning now to the adaptive systems and methods of the presentinvention, adaptation decision module 125 generally performs tests onthe current snapshot of sensor data or a sequence of these, to determinewhether or not to adapt to a new operational state of the process ormachine. This determination has inherent in it several more particulardecisions. First, the adaptation decision module must decide whether ornot the entire monitoring apparatus has just initiated monitoring ornot. If monitoring has just started, the adaptation decision module willwait for several snapshots or samples of data for the monitoring tostabilize before making tests to decide to adapt. A second decisionrelated to the overall decision to adapt pertains to whether or not themonitored process or machine has entered a transition or not. Typically,when a process or machine changes states, whether through process upset,machine failure, or merely a change in normal operation, there is aperiod of time during which the monitored sensors provide dynamic data,and the process or machine is neither stably in its old mode nor yetstably in its new target mode. This transition is usually manifested asa transient swing in one or more of the sensor data. The adaptationdecision module waits for the transition to complete before adapting.Therefore, in addition to the second decision of determining when atransition has begun, a third decision that must be made is whether thetransition period is over, and the monitored process or machine is in anew stable operational state. It should be understood that “stable” doesnot mean a state in which all sensor readings are flat, but rather astate that can be reliably recognized by the empirical model, which mayentail dynamic but nonetheless correlated movement of sensor readings. Afourth decision that must be made after a transition is to determine ifthe new stable operational state is one that has not been seen by theempirical model or not. If it has not before been encountered, it is acandidate for adaptation. Finally, a fifth decision that must be made iswhether a new, previously unencountered state is in fact a newacceptable state, or a process or sensor upset.

[0050] According to the invention, detection of a transient as evidenceof a possible transition out of the current operational state can beperformed using the global similarity operator. The global similarity isthe vector-to-vector similarity score computed from a comparison of thecurrent snapshot from the input bus 108 against the estimate from theestimation engine 111. Typically, the estimate is the estimate generatedin response to the current snapshot, but it is also within the scope ofthe present invention that it can be an estimate generated from a priorsnapshot, such as when the model generates predictive estimates forsensor values. The calculations for generating a vector-to-vectorsimilarity value have already been outlined above. Turning to FIG. 5, achart is shown of a typical global similarity generated for a process ormachine under monitoring. The vertical axis 501 is the global similarityscore, and the horizontal axis 504 is the snapshot or sample number ofthe input snapshots, which are typically sequential in time, but mayalso represent some other ordered presentation of snapshots. An upperlimit 506 and a lower limit 509 are calculated as described below foruse in determining at what point the global similarity line or signal512 indicates a transient. The global similarity score at 516 is showndropping below the limit 509, as are subsequent global similarityscores.

[0051] Generally, when a process or machine is operating in a state thatis recognized by the empirical model, the global similarity between theestimate and the current input are high, close to 1, and do not varymuch. The location of the limits 506 and 509 can be user-selected, orcan be automatically selected. One method for automatically selectingthese limits is to collect a series of successive global similaritiesand determine the mean of them and the standard deviation. The limitsare then set at the mean plus or minus a multiple of the standarddeviation. A preferred multiple is 3 times the standard deviation. Thenumber of successive global similarities used can be any statisticallysignificant number over which the process or machine is in a modeledoperational state, and 100-1000 is a reasonable number. A smaller numbermay be reasonable if the sampling rate for monitoring is lower, and insome cases can be in the range of 5-10 where the sampling rate formonitoring is on the order of single digits for the time period in whichthe monitored system or process can substantially deviate from normaloperation.

[0052] Yet another way of computing the limits 506 and 509 is asfollows. After accumulating a historic data set from which a referencelibrary is selected according to a training method like the Min-Maxmethod described with reference to FIGS. 2 and 3, the remainingsnapshots of the historic set that were not selected into the referencelibrary can be fed in as input to the empirical model, and the globalsimilarities for the estimates generated therefrom can be used. Theseprovide a mean and a standard deviation for setting the limits 506 and509 as described above.

[0053] According to yet another way of defining limits 506 and 509, theyare not straight line limits, but instead limits that float a fixedamount on either side of a mean determined over a moving window ofglobal similarities. For example, the standard deviation may be computedaccording to either way described above, and then a multiple of thestandard deviation selected. This is then set around a mean this isdefined as the mean global similarity of the last several snapshots, forexample the last five or the last ten.

[0054] When a global similarity at a snapshot 516 travels outside thelimits 506 or 509, the adaptation decision module recognizes this as atransient. This signifies a likelihood that a transition of themonitored process or machine is starting. The adaptation decision modulecan turn off monitoring, or at least alert generation from statisticaltesting module 122 upon detection of a transient. Further, theadaptation decision module then begins to employ one or more of severaltests that can be used to determine when a transition period ends.

[0055] Preferably, upon first detecting the transient, the adaptationdecision module places upper limit 506 and lower limit 509 around eachsubsequent global similarity point, using the point as the mean, butstill using the selected multiple of the prior established standarddeviation as the limits. Each successive point is compared to theselimits as set around the “mean” of the last point location. This can beseen in FIG. 6, which shows a process or machine coming out oftransition, as measured by global similarity. Point 602 is a transitionpoint. Upper limit 605 and lower limit 608 are shown at some multiple ofthe prior established standard deviation around the point 602. Point 611falls outside of this range, and therefore is also a transition point.However, point 614 falls within the range around point 617, and theadaptation decision module then begins to keep track of these two andsubsequent points to test for stability of the global similarity. Oneway of doing this is to count a successive number of snapshot globalsimilarities that all fall within the range around the prior globalsimilarity, and when a particular count is reached, determine theprocess or machine to have stabilized. A typical count that can be usedis five snapshots, though it will be contingent on the dynamics of theprocess or machine being monitored, and the sample rate at whichsnapshots are captured. Counting can start at either point 617 or 614.If a subsequent point falls outside of the range, before the chosencount is reached, such as is shown at point 620, the point is determinedto be in transition, and the count is zeroed. Starting at point 620then, the count would begin again if the point following were withinrange. Until the count is reached, the process or machine is consideredto still be in transition. Another way of determining if a the monitoredprocess or machine has stabilized in a new state is to look for at leasta selected number of global similarity scores over a moving window ofsnapshots that lie within the aforementioned range, where the range isset around the mean of all previous global similarities in the windowfor any given global similarity. By way of example, if the window ofsnapshots is five, and the selected number in the set of five that musthave qualifying global similarities in range is four, then the secondglobal similarity score qualifies if it lies in the range set around thefirst global similarity, and the third global similarity qualifies if itlies in the range set around the mean of the first and second globalsimilarities, and so on. If the four global similarities after the firstall qualify, then the system has stabilized in a new state. The windowcan be chosen to be much longer, 50 for example, depending on thesampling rate of monitoring, and the selected least number of qualifyingvalues can be 40 for example.

[0056] When a count is reached of in-range global similarity points, asfor example at point 623 after five consecutive in-range pointsindicated by box 625, the adaptation decision module indicates thetransition is over and a new state has been reached. Note in FIG. 6, theglobal similarity has stabilized at a lower overall similarity (around0.8) than was shown in FIG. 5 (around 0.975), indicating the empiricalmodel is not modeling this state as well as the previous state, and mayin fact not be recognizing the new state at all. Typically, if the newstate is also part of the empirical model, the global similarity curvewill look more like that shown in FIG. 7. Therein, a first operationalstate is indicated by global similarities 701. A transition is begun attransient 703, and continues until a new stable operational state 705 isreached beyond point 706 as indicated by five (or some other preselectednumber) of consecutive global similarities 710 within range of eachother.

[0057] According to yet another way for determining adaptation,independent of the use of the global similarity, the adaptation decisionmodule can examine certain of the sensor data that comprise the currentsnapshot that are designated by the user usually upon installation ascontrol variables in the monitored process or machine. This techniqueprovides a much simpler way of determining when to adapt, but can onlybe employed when control variables are clearly separable from dependentparameters of the process or machine. A control variable is typicallymanually determined ahead of model building with domain knowledge of theapplication. Control variables are typically those inputs to a processor machine that drive the operational behavior of the process ormachine. They are often environmental variables over which no controlcan be exerted. For example, in an engine or turbine, ambienttemperature is often a control variable. When training the empiricalmodel, as for example outlined above with the Min-Max method, thesoftware for executing the inventive adaptive monitoring system keepstrack of the overall ranges of the control variables seen in thetraining set from which the reference set is distilled. Then, inmonitoring operation, the adaptive decision module simply compares thecurrent control variable(s) to those ranges, and if one or more controlvariables are now outside the range trained on, the adaptation decisionmodule can initiate retraining. It is also useful to use controlvariables alongside the global similarity operator, so that adetermination can be made when the transition from one state to anotheris over, as described above. Alternatively, standard techniques known inthe art for analyzing the stability of variables can also be employeddirectly against the control variables, if the dynamics of the controlvariables permits, to make the determination of when a transition beginsand ends. In any case, in using control variables to determine when toretrain the empirical model, what is sacrificed is the ability tomonitor those control variables for upset. In other words, if a controlvariable goes outside the range that was trained on, it is assumed bythe inventive apparatus that a new acceptable operational state has beenencountered, rather than assuming that the control variable indicatesabnormal operation.

[0058] In the event that this control variable-based decision is notemployed, there remains after determining that a transition has stopped,the step of determining whether the new state is also alreadysufficiently modeled, or is a heretofore-unencountered state that mustbe adapted to. For this the adaptation decision module has a battery oftests that can be used to make the determination in addition to thecontrol variable range check.

[0059] In a first technique, a threshold may be applied to the meanglobal similarity of the new state at the end of the transition period.For example, with reference to FIG. 8, a mean lower than a 0.90threshold 804 can be used to indicate that the new state is notsufficiently modeled by the empirical model, and the model must beadapted to accommodate the new state. According to the invention, themean can be examined over one snapshot 808 to make this decision (inwhich case the mean is simply the global similarity), or alternativelycan be examined over a series of snapshots, where the mean is constantlyrecalculated using the most recent 5 results, by way of example. If themean then falls below the selected threshold more than a selectedfraction of snapshots over a series of snapshots (for example half),then the new state is considered to be unrecognized and potentiallysubject to adaptation. For example, as shown in FIG. 8 the five points812 have four that fall below the threshold 804, and only one above, andtherefore this state would be considered unrecognized.

[0060] According to a second technique, a window of successive globalsimilarity values can be compared to the selected threshold, and if atleast a certain number of these falls below the threshold, then the newstate is considered to be unrecognized and potentially subject toadaptation. For example, if a moving window of five global similaritiesare examined, and at least three are below the threshold, the new statecan be deemed subject to adaptation.

[0061] In a third technique depicted in FIGS. 9A and 9B, the actualcurrent snapshot can be processed for similarity against the entirereference library (as is done as part of the process of generating theestimate), and a test is performed on the similarities. Given that theadaptation decision module indicates a new state has been settled into,the similarity scores of the current snapshot against the referencelibrary can be examined for the highest such similarity, and if this isbelow a chosen threshold, the new state can be deemed an unrecognizedstate that is a candidate for adaptation. A typical threshold for thiswould be in the range of less than 0.90. As can be seen in FIG. 9A, uponcomparing the current snapshot 903 (symbolized by a vector symbol withdots standing in for sensor values) to the snapshots of the referencelibrary 114, a series of similarity scores 907 are generated for eachcomparison as part of routine monitoring. The scores are shown in achart in FIG. 9B, where a highest similarity score 912 is above the 0.90threshold, and therefore the current snapshot does not indicate a needto adapt. Again, this decision can be made in one snapshot, or can bemade by determining whether a selected fraction of more of a series ofcurrent snapshots have highest reference library similarities that fallbelow the chosen threshold.

[0062] Yet a third technique that may be employed to determine if a newstate presents itself and the empirical model must be adapted is toexamine the alarm fraction generated by a SPRT module on the monitoringapparatus.

[0063] According to the invention, the global similarity operator hasthe inherent ability to distinguish between a process or sensor upsetand a change of state. When a sensor fails, the empirical modeltypically estimates a reasonable value for what the sensor ought toindicate, based on the other input sensors. The difference between thisfailed sensor reading and the estimate for it (really an estimate of theunderlying measured parameter) provides a means for statistical testingmodule 122 to alert a human operator that there is a problem at thefailed sensor. However, due to the nature of the similarity operation,the effect on the global similarity is limited. In fact, the mean ofseveral sequential global similarities in the case of a failed sensormay not change much from the mean when the sensor was not failed, thoughthe variance of the global similarity may increase somewhat (yet usuallystill remain within the thresholds 506 and 509 indicated in FIG. 5). Inthis way, the adaptation decision module will generally not attempt toadapt on a failed sensor, and the monitoring system can successfullyalert on the failed sensor.

[0064] When a process upset occurs that affects one or only a few of themonitored parameters, the adaptation decision module will similarly notindicate the need to adapt, even though alerts for the upset areoccurring in the monitoring apparatus. This is true even where a processupset eventually leads to significant change in all the variables,because the monitoring apparatus of the present invention is designed tocatch the earliest possible sign of change and alert on it. Long beforethe process upset affects all variables, it is likely the human operatorwould have been notified of the upset.

[0065] In addition, a catastrophic process upset usually also fails toexhibit a settling into a new state. Global similarities for a severelyupset process not only potentially drop to very low levels (less than0.50) but also suffer from a continuing large variance. Typically, aprocess upset will fail to settle into a new stable state with therapidity that a mere operational mode shift will, and this can be usedto distinguish a process upset from a new acceptable operational state.This is best determined empirically based on the application, and a userselectable setting can be provided in the software of the adaptationdecision module to designate a period during which a transition mustsettle into a stable state or otherwise be considered a process upsetand turn on alerting again. According to the invention, the adaptationdecision module can also measure the variance of the global similarity,and if the variance is still above a certain threshold after a selectedtimeout period, the transition can be deemed a process upset, and againalerting can be turned back on in the monitoring coming throughstatistical testing module 122.

[0066] After the adaptation decision module has ascertained that:

[0067] 1) a control variable is now out of range, and adaptation iswarranted because:

[0068] a) the global similarity is now below an acceptable threshold,indicating a new unrecognized state; or

[0069] b) the highest similarity of the current snapshot or sequence ofsnapshots is below an acceptable threshold, indicating a newunrecognized state; or

[0070] c) a number of alerts are being generated, startingcoincidentally with the change in the control variable; or

[0071] 2) an adaptation is warranted because:

[0072] a) a transient was detected on global similarity, signaling atransition; and

[0073] b) the transition completed and a new stable state was realized;and

[0074] i) the new stable state is not recognized because the globalsimilarity is now below an acceptable threshold; or

[0075] ii) the new stable state is not recognized because the highestsimilarity of the current snapshot or sequence of snapshots is below anacceptable threshold; or

[0076] iii) the new stable state is not recognized because of thefraction of alerts that are being generated in monitoring is above athreshold.

[0077] An adaptation step is then carried out by the retrain module 128.According to the invention, retraining can be accomplished either byadding snapshots from the sequence of current snapshots to the referencelibrary, or by replacing snapshots in the reference library. Both modescan be used, where the reference library has an initial size atimplementation of the monitoring system, and a maximum size is selectedto which the reference library can grow, and beyond which newly addedsnapshots must replace existing snapshots.

[0078] When adding current snapshots to the reference library, theretrain module first decides which snapshots to select for addition.According to one embodiment, when the adaptation decision moduleidentifies based on the global similarity a sequence of several, e.g., 5snapshots, for which the global similarity has stabilized, that is a newstate, and the new state has been determined to be previously unmodeled,the five snapshots can be used to augment the reference library. Inaddition, as of the sixth snapshot, the retrain module begins to go intoa longer adaptation cycle, checking the snapshots as they come in andtesting using the global similarity test whether the newly augmentedmodel is adequately modeling the new snapshots. A threshold can again bedetermined, for example 0.90, which the newly augmented referencelibrary must surpass in global similarity, for the adaptation to bedeclared finished. If the threshold is not met, then the retrain modulecontinues to add new snapshots (or at least those snapshots which do notappear to be adequately modeled) as long as the new state is stable andnot a new transient (indicating a new stage of transition or perhapsprocess upset or sensor failure. A set limit to how long a retrainmodule will continue to engage in the longer adaptation cycle beyond theend of a transition can also optionally be set, so that adaptation doesnot continue indefinitely. This may apply to a new state which simplycannot be adequately modeled to the global similarity threshold chosenas the cutoff for adaptation.

[0079] According to yet another mode, instead of merely adding theadditional identified snapshots to the reference library, the entirereference library and the additional snapshots can be combined into atotal training set to which a training method such as Min-Max isapplied, to distill the new training set into a new reference library.

[0080] When the size limit on the reference library is reached, thevector removal module can use several methods to replace or remove oldsnapshots (or vectors of sensor data) from the reference library.According to a first way, for each snapshot that will be added beyondthe limit, the vector in the reference library which bears the highestsimilarity to the snapshot desirably added is removed. For thisoperation the similarity operator is used as described herein. Accordingto a second method, upon using a training method such as Min-Max, thetime stamp of when a vector is added to the reference library isexamined through the entire library, and the oldest time stamped vectoris removed. In this case, the replacement snapshot bears the time stampof the moment of replacement, and therefore has the newest time stamp.According to yet another method, during regular monitoring mode of theempirical model-based monitoring apparatus, for each current snapshotfrom the monitored process or machine, a determination is made whichsnapshot in the reference library has the highest similarity to it, andthat snapshot is time-stamped with the moment of comparison. Therefore,each snapshot in the reference library is potentially being updated asbeing the last closest state vector seen in operation of the process ormachine. Then, when adding a new vector as part of adaptation, thevector with the oldest time stamp is replaced. The new replacementsnapshot of course bears a current time stamp. In this way, snapshots inthe reference library representing states the monitoring system has notseen in the longest time, are replaced first with new updated snapshots.This mode is particularly useful when monitoring equipment or processesthat settle gracefully with age, and are not expected to achieve exactlythe operational states they were in when they were brand new.

[0081] It will be appreciated by those skilled in the art thatmodifications to the foregoing preferred embodiments may be made invarious aspects. The present invention is set forth with particularityin any appended claims. It is deemed that the spirit and scope of thatinvention encompasses such modifications and alterations to thepreferred embodiment as would be apparent to one of ordinary skill inthe art and familiar with the teachings of the present application.

What is claimed is:
 1. A method for adapting an empirical model used inmonitoring a system, comprising the steps of: receiving actual values ofmonitored parameters characterizing the system; generating from theempirical model estimates of the parameter values in response toreceiving actual values; calculating a global similarity score for acomparison of a set of estimated parameter values and a related set ofactual parameter values; and adapting the empirical model to account forat least some received actual values based on the global similarityscore.
 2. A method according to claim 1 where said adapting stepcomprises adapting the empirical model when a global similarity scorefalls outside of a selected range.
 3. A method according to claim 1where in the adapting step comprises: identifying a beginning of atransition phase when a global similarity score falls outside of aselected range; identifying an end of the transition phase; anddetermining in response to identification of the end of the transitionphase whether the system is in a new state not accounted for in theempirical model; and updating the empirical model to account for the newstate in response to a determination that the new state was notaccounted for in the empirical model.
 4. A method according to claim 3wherein the determining step comprises comparing at least one globalsimilarity score after the end of the transition phase to a thresholdand if it is below the threshold then concluding that the new state isnot accounted for in the empirical model.
 5. A method according to claim3 wherein the determining step comprises comparing a window of globalsimilarity scores after the end of the transition phase to a thresholdand if at least a selected number of said scores in said window fallbelow the threshold then concluding that the new state is not accountedfor in the empirical model.
 6. A method according to claim 3 wherein thedetermining step comprises comparing the mean of a window of globalsimilarity scores after the end of the transition phase to a thresholdand if the mean of said scores in said window falls below the thresholdthen concluding that the new state is not accounted for in the empiricalmodel.
 7. A method according to claim 3 wherein the empirical model hasa reference library of snapshots of parameter values characterizingrecognized system states, and the determining step comprises comparing asnapshot of received actual values after the end of the transition phaseto each snapshot in the reference library to compute a similarity foreach comparison, and if the highest such similarity is less than aselected threshold then concluding that the new state is not accountedfor in the empirical model.
 8. A method according to claim 3 wherein theempirical model has a reference library of snapshots of parameter valuescharacterizing recognized system states, and the determining stepcomprises comparing each in a series of snapshots of received actualvalues after the end of the transition phase to each snapshot in thereference library to compute a similarity for each comparison, and ifthe mean over the series of the highest similarity for each actualsnapshot is less than a selected threshold then concluding that the newstate is not accounted for in the empirical model.
 9. A method accordingto claim 3 wherein the empirical model has a reference library ofsnapshots of parameter values characterizing recognized system states,and the determining step comprises comparing each in a series ofsnapshots of received actual values after the end of the transitionphase to each snapshot in the reference library to compute a similarityfor each comparison, and if the highest similarity of at least aselected number of actual snapshots over the series is less than aselected threshold then concluding that the new state is not accountedfor in the empirical model.
 10. A method according to claim 3, whereinthe step of identifying the end of the transition phase comprisesexamining a moving window of successive global similarity scores andwhen each of at least a selected number of successive global similarityscores in the window lies within a selected range around the previousglobal similarity score, identifying that the end of transition has beenreached.
 11. A method according to claim 3, wherein the step ofidentifying the end of the transition phase comprises examining a movingwindow of successive global similarity scores and when each of at leasta selected number of successive global similarity scores in the windowlies within a selected range around the mean of the previous globalsimilarity scores in the window, identifying that the end of transitionhas been reached.
 12. A method according to claim 3 wherein theempirical model has a reference library of snapshots of parameter valuescharacterizing recognized system states, and the updating step comprisesadding at least one snapshot of the received actual values to thereference library.
 13. A method according to claim 1 wherein theselected range has a lower threshold equal to a multiple of a standarddeviation for a sequence of global similarity scores, subtracted fromthe mean of the sequence of global similarity scores.
 14. A methodaccording to claim 1 wherein the calculating step comprises comparingcorresponding elements of a snapshot of received actual parameter valuesand a related snapshot of estimates to generate elemental similarities,and statistically combining the elemental similarities to generate theglobal similarity score.
 15. A method for adapting a reference data setof an empirical model used in empirically modeling a system, comprisingthe steps of: receiving actual values of monitored parameterscharacterizing the system, including at least one control parameter;determining that the actual value for the at least one control parameterlies outside a predetermined range; adapting the empirical model inresponse to said determining step, to account for the received actualvalues.
 16. A method according to claim 15 wherein the reference dataset comprises snapshots of time-correlated parameter values, and saidadapting step comprises adding at least one snapshot of the receivedactual values to the reference set.
 17. An apparatus for monitoring theoperation of a system characterized by operational parameters,comprising: an empirical model for generating estimates of parametervalues in response to receiving actual parameter values characterizingthe operation of the system; a global similarity engine for generating aglobal similarity score for a comparison of a set of estimated parametervalues and a related set of actual parameter values from said system;and an adaptation module for adapting the empirical model to account forat least some received actual parameter values based on the globalsimilarity score.
 18. An apparatus according to claim 17 where saidadaptation module is disposed to adapt the empirical model when a globalsimilarity score falls outside of a selected range.
 19. An apparatusaccording to claim 18 where said empirical model comprises a referencelibrary of snapshots of time-correlated parameter values, and saidadaptation module adapts the empirical model by adding at least onesnapshot of the received actual values to the reference library.
 20. Anapparatus according to claim 17 wherein the adaptation module firstidentifies a transition phase after which it adapts the empirical modelto account for at least some received actual parameter values based onglobal similarity scores from said global similarity engine.
 21. Anapparatus according to claim 20 wherein the adaptation module identifiesa beginning of the transition phase when a global similarity score fallsoutside of a selected range.
 22. A method according to claim 20, whereinthe adaptation module identifies the end of the transition phase byexamining a moving window of successive global similarity scores andwhen each of at least a selected number of successive global similarityscores in the window lies within a selected range around the previousglobal similarity score, identifying that the end of transition has beenreached.
 23. A method according to claim 20, wherein the adaptationmodule identifies the end of the transition phase by examining a movingwindow of successive global similarity scores and when each of at leasta selected number of successive global similarity scores in the windowlies within a selected range around the mean of the previous globalsimilarity scores in the window, identifying that the end of transitionhas been reached.
 24. An apparatus according to claim 20 wherein theadaptation module determines in response to identification of thetransition phase whether the system is in a new state not accounted forin the empirical model
 25. An apparatus according to claim 24 whereinthe adaptation module determines that the new state is not accounted forin the empirical model if at least one global similarity score after theend of the transition phase is below a selected threshold.
 26. Anapparatus according to claim 24 wherein the adaptation module determinesthat the new state is not accounted for in the empirical model if atleast a selected number of global similarity scores in a window ofglobal similarity scores after the end of the transition phase fallbelow a selected threshold.
 27. An apparatus according to claim 24wherein the adaptation module determines that the new state is notaccounted for in the empirical model if the mean global similarity valueover a window of global similarity scores after the end of thetransition phase falls below a selected threshold.
 28. An apparatusaccording to claim 24 wherein the empirical model comprises a referencelibrary of snapshots of parameter values characterizing recognizedsystem states, and the adaptation module compares a snapshot of receivedactual values after the end of the transition phase to each snapshot inthe reference library to compute a similarity for each comparison, andif the highest such similarity is less than a selected threshold thendetermines that the new state is not accounted for in the empiricalmodel.
 29. An apparatus according to claim 24 wherein the empiricalmodel comprises a reference library of snapshots of parameter valuescharacterizing recognized system states, and the adaptation modulecompares each in a series of snapshots of received actual values afterthe end of the transition phase to each snapshot in the referencelibrary to compute a similarity for each comparison, and if the meanover the series of the highest similarity for each actual snapshot isless than a selected threshold then determines that the new state is notaccounted for in the empirical model.
 30. An apparatus according toclaim 24 wherein the empirical model comprises a reference library ofsnapshots of parameter values characterizing recognized system states,and the adaptation module compares each in a series of snapshots ofreceived actual values after the end of the transition phase to eachsnapshot in the reference library to compute a similarity for eachcomparison, and if the highest similarity of at least a selected numberof actual snapshots over the series is less than a selected thresholdthen determines that the new state is not accounted for in the empiricalmodel.
 31. An apparatus according to claim 21 wherein the selected rangehas a lower threshold equal to a multiple of a standard deviation for asequence of global similarity scores, subtracted from the mean of thesequence of global similarity scores.
 32. A computer program product formonitoring the operation of a system characterized by operationalparameters, comprising: computer readable program code means forreceiving actual parameter values characterizing operation of thesystem, including at least one control parameter; computer readableprogram code means for determining that an actual value for the at leastone control parameter lies outside a predetermined range; data storagemeans for storing data representing an empirical model of the system;and computer readable program code means for adapting the storedempirical model data in response to said determining step, to accountfor the received actual values.
 33. A computer program product accordingto claim 32 wherein the empirical model data comprises snapshots oftime-correlated parameter values, and said means for adapting isdisposed to add at least one snapshot of the received actual parametervalues to the empirical model data.
 34. A computer program productaccording to claim 33 further comprising computer readable program meansfor generating estimates of parameter values in response to the meansfor receiving, using the empirical model data in said data storagemeans.
 35. A computer program product according to claim 34 wherein saidmeans for estimating uses a similarity operator.